Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada.     

Known, Unknown, and Unknowable Uncertainties

In normative decision theory, the weight of an uncertain event in a decision is governed solely by the probability of the event. A large body of empirical research suggests that a single notion of probability does not accurately capture peoples' reactions to uncertainty. As early as the 1920s, Knight made the distinction between cases where probabilities are known and where probabilities are unknown. We distinguish another case –- the unknowable uncertainty –- where the missing information is unavailable to all. We propose that missing information influences the attractiveness of a bet contingent upon an uncertain event, especially when the information is available to someone else. We demonstrate that the unknowable uncertainty –- falls in preference somewhere in between the known and the known uncertainty.     

Anxiety and Decision Making with Delayed Resolution of Uncertainty

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker may want to include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions.     

Improving decision‐making in care order proceedings: A multijurisdictional study of court decision‐makers' viewpoints

Child welfare removals of children are among the most invasive decisions a state can make toward its citizens, and typically it is the courts that make these decisions. These interventions are regularly exposed to criticism. In this paper, we examine if and how care order proceedings could be improved in England, Finland, Norway, and California, USA. We have asked the judiciary decision‐makers about their view on what should be improved. Our findings show that the organization of the proceedings, including time and staff, are identified as issues in all four systems. Furthermore, the preparations by the child welfare agency are also mentioned as an issue, for English, Finnish, and Californian decision‐makers. Very few decision‐makers indicate features related to the individual, situational, and contextual dimensions, which is interesting since this would be expected from organization theory. The strong call for change in the way proceedings are organized indicates a need for modernization as well as better use of available competency from child development experts. The respondents focus on the elements that a decision‐maker has direct experience with and knowledge about, and this is indeed worth noting for policymakers in the four systems.     

A note on decisions under uncertainty: the impact of the choice of the welfare measure

The paper addresses the question, how policy decisions under uncertainty depend on the underlying welfare concept. We study three different welfare measures: The first is directly based on the ex ante (expected) utility of a representative consumer whereas the second relies on an ex ante and the third on an ex post valuation of policy changes compared to the status quo. We show that decisions based on these measures coincide if and only if risk-neutral expected utility maximization is applied. Differences between the decisions are analyzed for both, risk-averse expected utility maximization and the MaxiMin criterion. For risk-averse decision makers, differences between the first and the second concept arise if the absolute risk-aversion of the decision maker is not constant in income. For risk-aversion and the MaxiMin criterion, the effort levels to provide a public good based on an optimization of ex post utility changes exceed those based on the first or second concept. Implications for environmental policy decisions based on the concepts of abatement costs and benefits from abatement are discussed.     

Why the Young Do Not Buy Long-Term Care Insurance

This paper explains why those individuals who purchase long-term care insurance usually postpone their decision until they reach the age of retirement. This behavior is shown to be rational if there are fixed costs of loading or if there is uncertainty about the costs of disability. Individuals with a low risk of becoming disabled before retirement may prefer to buy insurance late in order to avoid losses in expected income. However, if the probability of becoming disabled after retirement is uncertain, it is generally preferable to buy long-term care insurance early.     

The Diversification Theorem Restated: Risk-pooling Without Assignment of Probabilities

Bayesian decision theory assumes that agents making choices assign subjective probabilities to outcomes, even in cases where information on probabilities is obviously absent. Here we show that agents that presume that they are equal risks can share risks mutually beneficially, even if the probabilities of losses are unpredictable or genuinely uncertain. We show also that different risk aversions among pool members do not exclude mutually beneficial loss sharing at uncertainty. Sharing when individuals’ losses differ in probabilities or in amount may still make individuals better off. Our findings are related to the theory of the insurance firm, to the management of development risks, and to the theory of justice.JEL Classification: D8, G22, L10, L30     

A further exploration of the uncertainty effect

Individual valuation of a binary lottery at values less than the lottery’s worst outcome has been designated as the “uncertainty effect”. Our paper aims to explore the boundary conditions of the uncertainty effect by investigating a plausible underlying process and proposing two possible methods. First, we examine how providing an exogenous evaluation opportunity prior to judging the value of the lottery affects individuals’ judgments, and find that first valuing the worst outcome and then the lottery eliminates the uncertainty effect. Second, we explore whether introducing additional cognitive load dampens how far decision makers correct their initial evaluations, and find that additional cognitive load is able to eliminate the uncertainty effect.     

Risk Premiums and Benefit Measures for Generalized-Expected-Utility Theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumptions on functional form beyond the basic requirements of monotonicity, transitivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophistication. The approach relies on the distance and benefit functions to characterize preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative risk premiums and to characterize preferences exhibiting constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA). A generalization of the notion of Schur-concavity is presented. If preferences are generalized Schur concave, the absolute and relative risk premiums are generalized Schur convex, and the certainty equivalents are generalized Schur concave.     

The Aversion to the Sequential Resolution of Uncertainty

This paper sets forth and offers an explanation for preferences for the form of the timing of resolution of uncertainty; namely for uncertainty to be resolved all at one time rather than sequentially. The explanation is based on a weakening of the independence axiom, in particular on the notion of disappointment aversion developed in Gul's (1991) axiomatic model of preferences. Implications of this aversion are discussed for issues in finance, intertemporal decision making under uncertainty, high stakes risky situations and consumer self-regulation. The analysis encourages a formulation of preferences over all attributes of interest to the decision maker, including psychological satisfaction.     

On the Application of Multiattribute Utility Theory to Models of Choice

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are in conflict with either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example.      

Is specialization desirable in committee decision making?

Committee decision making is examined in this study focusing on the role assigned to the committee members. In particular, we are concerned about the comparison between committee performance under specialization and non-specialization of the decision makers. Specialization (in the context of project or public policy selection) means that the decision of each committee member is based on a narrow area, which typically results in the acquirement and use of relatively high expertise in that area. When the committee members’ expertise is already determined, specialization only means that the decision of each committee member is based solely on his/her relatively high expertise area. This form of specialization is potentially inferior relative to non-specialization under which the decision of each committee member is based on different areas, not just his/her relatively high expertise area. Given that the expertise of the committee members is already determined but unknown, our analysis focuses on non-specializing individuals whose decision is based on a decision rule that does not require information on the decision-making skills. Under these realistic assumptions, non-specialization is shown to be preferable over specialization, depending on the aggregation rule applied by the committee. The significance of our approach is not limited to the specific results that we obtain. Rather, it should be viewed as a first step toward a deeper examination of the role of individual decision makers in enhancing the performance of collective decision making.     

The impossibility of experimental elicitation of subjective probabilities

We show that if decision makers may have stakes in certain events then the experimental elicitation of their subjective probabilities of these events is impossible.We thank Eyal Sulganik for helpful comments on an earlier draft of this paper.     

Uncertainty aversion and aversion to increasing uncertainty

According to the original Ellsberg (1961) examples there is uncertainty version if the decision maker prefers to bet on an urn of known composition rather than on an urn of unknown composition. According to another definition (Schmeidler, 1989), there is uncertainty aversion if any convex combination of two acts is preferred to the least favorable of these acts. We show that these two definitions differ: while the first one truly refers to uncertainty aversion, the second one refers to aversion to increasing uncertainty. Besides, with reference to Choquet Expected Utility theory, uncertainty aversion means that there exists the core of a capacity, while aversion to increasing uncertainty means that the capacity is convex. Consequently, aversion to increasing uncertainty implies uncertainty aversion, but the opposite does not hold. We also show that a completely analogous situation holds for the case of risk and we define a set of risk and uncertainty premiums according to the previous analysis.     

Sequential decision making without independence: a new conceptual approach

This paper presents a critical reflection on dynamic consistency as commonly used in economics and decision theory, and on the difficulty to test it experimentally. It distinguishes between the uses of the term dynamic consistency in order to characterize two different properties: the first accounts for the neutrality of individual preferences towards the timing of resolution of uncertainty whereas the second guarantees that a strategy chosen at the beginning of a sequential decision problem is immune to any reevaluation and will effectively be implemented from then on in the decision problem. Although these two properties are equivalent under expected utility (EU), this is not the case under non-EU. Building on the possible characteristics of individual dynamic preferences under risk, this paper proposes a conceptual categorization, that is experimentally testable, of possible sequential decision making behaviors of non-EU maximizers.     

Ambiguity and the value of information

The value of information is studied in a non-expected utility model of ambiguity with second-order probabilities. Information that reduces ambiguity has a positive value for ambiguity-averse decision makers, and the value of information that resolves ambiguity increases with greater ambiguity and with greater ambiguity aversion. Since information that resolves risk is valuable, and must also resolve ambiguity, the value of such information for ambiguity averters increases with greater ambiguity and with greater ambiguity aversion.     

The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker??s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.     

Action Bias and Environmental Decisions

Individuals have a penchant for action, often for good reasons. But action bias arises if that penchant is carried over to areas where those reasons do not apply, hence is nonrational. Action bias is explored theoretically, and then empirically, using data from surveys of hypothetical environmental decisions. Quite apart from agency considerations, individuals like to affect outcomes when gains are reaped. Given the ability to help one of two sites, we find that decision makers choose to foster improvement rather than prevent deterioration, despite framing that makes it arbitrary which site is improved, which preserved. Strong action bias—individuals choosing to reap gains even though they must impose losses—is also observed. These concepts are related to loss aversion, status quo bias, omission bias for losses, and bright-line behavior.